You'll earn points on your stays booked through the Marriott website or by calling reservations. See item 8 in the terms under Earning, http://www.marriott.com/rewards/terms/earning.mi for details.
Sadly, I just found this out. Booked through a travelsite (flight plus stay) in St. Thomas, only to be told by Marriott that this stay does not count for awards. The marriott website , in my view, is misleading, by stating
Earn for every stay. Depending on the hotel, you may earn up to 10 points or 2 air miles for every US dollar spent on your room rate or your total bill.
the disclaimer one can only find embedded in the fine print of rules. The above statement should be modified to say "Earn for every stay booked through the Marriott website".